Annual percentage rate of charge (APR), corresponding sometimes to a nominal APR and sometimes to an effective APR (EAPR), is the interest rate for a whole year (annualized), rather than just a monthly fee/rate, as applied on a loan, mortgage loan, credit card, etc. It is a finance charge expressed as an annual rate. Those terms have formal, legal definitions in some countries or legal jurisdictions, but in the United States: The nominal APR is the simple-interest rate (for a year). The effective APR is the fee+compound interest rate (calculated across a year). "Subject: Regulation AA", Alfred F."Bob" Blair, Jr., US Federal Reserve, 2008-06-28, webpage: US-Federal-Reserve-R1314.
In some areas, the annual percentage rate (APR) is the simplified counterpart to the effective interest rate that the borrower will pay on a loan. In many countries and jurisdictions, lenders (such as banks) are required to disclose the "cost" of borrowing in some standardized way as a form of consumer protection. The (effective) APR has been intended to make it easier to compare lenders and loan options.
Multiple definitions of effective APR The nominal APR is calculated by multiplying the interest rate for a payment period by the number of payment periods in a year. However, the exact legal definition of "effective APR", or EAR, can vary greatly in each jurisdiction, depending on the type of fees included, such as participation fees, loan origination fees, monthly service charges, or late fees. The effective APR has been called the "mathematically-true" interest rate for each year. "The Financial Literacy Crisis", April 2008, U.S. News & World Report, webpage: USNews-Your-Money-101. "President's Advisory Council on Financial Literacy", January 2008, Rossputin.com, webpage: Rossputin-FinLiteracy.
The computation for the effective APR, as the fee + compound interest rate, can also vary depending on whether the up-front fees, such as origination or participation fees, are added to the entire amount, or treated as a short-term loan due in the first payment. When start-up fees are paid as first payment(s), the balance due might accrue more interest, as being delayed by the extra payment period(s). "Margill – Loans, Lines of credit, APR" (calculation types), Margill/Jurismedia inc., 2008, webpage: Margill-en.
Effective annual percentage rate can be computed in at least three ways: by compounding the interest rate for each year, without considering fees; origination fees are added to the balance due, and the total amount is treated as the basis for computing compound interest; the origination fees are amortized as a short-term loan. This loan is due in the first payment(s), and the unpaid balance is amortized as a second long-term loan. The extra first payment(s) is dedicated to primarily paying origination fees and interest charges on that portion.
For example, consider a $100 loan which must be repaid after one month, plus 5%, plus a $10 fee. If the fee is not considered, this loan has an effective APR of approximately 80% (1.0512 = 1.7959, which is approximately an 80% increase). If the $10 fee were considered, the monthly interest increases by 10% ($10/$100), and the effective APR becomes approximately 435% (1.1512 = 5.3503, which equals a 435% increase). Hence there are at least two possible "effective APRs": 80% and 435%. Laws vary as to whether fees must be included in APR calculations.
United States In the United States, the Truth in Lending Act governs the calculation and disclosure of APR, implemented by the Consumer Financial Protection Bureau (CFPB) through Regulation Z. In general, APR in the United States is expressed as the periodic (for instance, monthly) interest rate times the number of compounding periods in a yearhttps://web.archive.org/web/20051103034219/http://www.uncdf.org/mfdl/readings/EIR_Tucker.pdf Tucker, William R. "Effective Interest Rate," Paper, Bankakademie Micro Banking Competence Center, 5–6 September 2000. (also known as the nominal interest rate); since the APR must include certain non-interest charges and fees, it requires more detailed calculation. The APR must be disclosed to the borrower within 3 days of applying for a mortgage. This information is typically mailed to the borrower and the APR is found on the truth in lending disclosure statement, which also includes an amortization schedule.
On July 30, 2009, provisions of the Mortgage Disclosure Improvement Act of 2008 (MDIA) came into effect. A specific clause of this act refers directly to APR disclosure on mortgages. It states, if the final annual percentage rate APR is off by more than 0.125% from the initial GFE disclosure, then the lender must re-disclose and wait another three business days before closing on the transaction.
The calculation for "close-ended credit" (such as a home mortgage or auto loan) can be found here. For a fixed-rate mortgage, the APR is thus equal to its internal rate of return (or yield) under an assumption of zero prepayment and zero default. For an adjustable-rate mortgage the APR will also depend on the particular assumption regarding the prospective trajectory of the index rate.
The calculation for "open-ended credit" (such as a credit card, home equity loan or other line of credit) can be found here.
European Union The European Union's APR standardization focuses on transparency and consumer rights: «a comprehensible set of information to be given to consumers in good time before the contract is concluded and also as part of the credit agreement [...] every creditor has to use this form when marketing a consumer credit in any Member State» so marketing different figures is not allowed.
The EU regulations were reinforced with directives 2008/48/EC and 2011/90/EU, fully in force in all member states since 2013. However, in the UK the EU directive has been interpreted as the Representative APR.
A single method of calculating the APR was introduced in 1998 (directive 98/7/EC) and is required to be published for the major part of loans. Using the improved notation of directive 2008/48/EC, the basic equation for calculation of APR in the EU is:
where: M is the total number of drawdowns paid by the lender N is the total number of repayments paid by the borrower i is the sequence number of a drawdown paid by the lender j is the sequence number of a repayment paid by the borrower Ci is the cash flow amount for drawdown number i Dj is the cash flow amount for repayment number j ti is the interval, expressed in years and fractions of a year, between the date of the first drawdown* and the date of drawdown i sj is the interval, expressed in years and fractions of a year, between the date of the first drawdown* and the date of repayment j. The EU formula uses the natural convention that all time intervals in ti and sj are measured relative to the date of the first drawdown, hence t1 = 0. However, any other date could be used without affecting the calculated APR, as long as it is used consistently: an offset applied to all times simply scales both sides of the equation by the same amount, without affecting the solution for APR.
In this equation the left side is the present value of the drawdowns made by the lender and the right side is the present value of the repayments made by the borrower. In both cases the present value is defined given the APR as the interest rate. So the present value of the drawdowns is equal to the present value of the repayments, given the APR as the interest rate.
Note that neither the amounts nor the periods between transactions are necessarily equal. For the purposes of this calculation, a year is presumed to have 365 days (366 days for leap years), 52 weeks or 12 equal months. As per the standard: "An equal month is presumed to have 30.41666 days (i.e. 365/12) regardless of whether or not it is a leap year." The result is to be expressed to at least one decimal place. This algorithm for APR is required for some but not all forms of consumer debt in the EU. For example, this EU directive is limited to agreements of €50,000 and below and excludes all mortgages.
In the Netherlands the formula above is also used for mortgages. In many cases the mortgage is not always paid back completely at the end of period N, but for instance when the borrower sells his house or dies. In addition, there is usually only one payment of the lender to the borrower: in the beginning of the loan. In that case the formula becomes:
where: S is the borrowed amount or principal amount. A is the prepaid onetime fee R the rest debt, the amount that remains as an interest-only loan after the last cash flow.
If the length of the periods are equal (monthly payments) then the summations can be simplified using the formula for a geometric series. Either way, the APR can be solved iteratively only from the formulas above, apart from trivial cases such as N=1.
Additional considerations Confusion is possible in that if the word "effective" is used separately as meaning "influential" or having a "long-range effect", then the term effective APR will vary, as it is not a strict legal definition in some countries. The APR is used to find compound and simple interest rates. APR is also an abbreviation for "Annual Principal Rate" which is sometimes used in the auto sales in some countries where the interest is calculated based on the "Original Principal" not the "Current Principal Due", so as the Current Principal Due decreases, the interest due does not.
Rate format
An effective annual interest rate of 10% can also be expressed in several ways: 0.7974% effective monthly interest rate, because 1.00797412=1.1 9.569% annual interest rate compounded monthly, because 12×0.7974=9.569 9.091% annual rate in advance, because (1.1-1)÷1.1=0.09091
These rates are all equivalent, but to a consumer who is not trained in the mathematics of finance, this can be confusing. APR helps to standardize how interest rates are compared, so that a 10% loan is not made to look cheaper by calling it a loan at "9.1% annually in advance".
The APR does not necessarily convey the total amount of interest paid over the course of a year: if one pays part of the interest prior to the end of the year, the total amount of interest paid is less.
In the case of a loan with no fees, the amortization schedule would be worked out by taking the principal left at the end of each month, multiplying by the monthly rate and then subtracting the monthly payment.
This can be expressed mathematically by
where: p is the payment made each period P0 is the initial principal r is the percentage rate used each payment n is the number of payments
This also explains why a 15-year mortgage and a 30-year mortgage with the same APR would have different monthly payments and a different total amount of interest paid. There are many more periods over which to spread the principal, which makes the payment smaller, but there are just as many periods over which to charge interest at the same rate, which makes the total amount of interest paid much greater. For example, $100,000 mortgaged (without fees, since they add into the calculation in a different way) over 15 years costs a total of $193,429.80 (interest is 93.430% of principal), but over 30 years, costs a total of $315,925.20 (interest is 215.925% of principal).
In addition the APR takes costs into account. Suppose for instance that $100,000 is borrowed with $1000 one-time fees paid in advance. If, in the second case, equal monthly payments are made of $946.01 against 9.569% compounded monthly then it takes 240 months to pay the loan back. If the $1000 one-time fees are taken into account then the yearly interest rate paid is effectively equal to 10.31%.